Flavor-energy uncertainty relations for neutrino oscillations in quantum field theory

Massimo Blasone,Luca Smaldone,Petr Jizba

doi:10.1103/physrevd.99.016014

Abstract

In the context of quantum field theory, we derive flavor energy uncertainty relations for neutrino oscillations. By identifying the non conserved flavor charges with the clock observables, we arrive at the Mandelstam Tamm version of time energy uncertainty relations. In the ultrarelativistic limit these relations yield the well known condition for neutrino oscillations. Ensuing non relativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of Fock spaces for flavor and massive neutrinos, are also discussed.

Highlights

Neutrino mixing and oscillations represent one of the most pressing challenges of modern theoretical and experimental particle physics
By identifying the nonconserved flavor charges with the “clock observables,” we arrive at the Mandelstam-Tamm version of time-energy uncertainty relations
While the quantum mechanical (QM) description [4,5,6] is quite successful in tackling high-energy features of neutrino oscillations, the corresponding quantum field theoretical (QFT) description is still controversial [6,7,8,9]

Summary

INTRODUCTION

Neutrino mixing and oscillations represent one of the most pressing challenges of modern theoretical and experimental particle physics They were first introduced by Pontecorvo [1] in a close analogy with the phenomenon of Kaon oscillations [2], and subsequently confirmed in a number of experimental settings [3]. [15], it was shown that for neutrino oscillations described in terms of Pontecorvo states, the MandelstamTamm time-energy uncertainty relations (TEUR) [16] reduce to the known condition for neutrino oscillations [4]. This result was obtained in the context of standard perturbative treatment of neutrino flavor states. For simplicity’s sake, confined to two flavors only, the results obtained can be extended to three flavors including CP violation

NEUTRINO MIXING AND OSCILLATIONS IN QFT

MANDELSTAM-TAMM TEUR

TEUR FOR NEUTRINO OSCILLATIONS IN QFT

CONCLUSIONS